Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

Annals of Global Analysis and Geometry

Volumn 41, Issue 4, 2012, Pages 461-472

  Bauer, Martin ^a   Bruveris, Martins ^b   Harms, Philipp ^a   Michor, Peter W ^a  

^a UNIVERSITY OF VIENNA   (Austria)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Diffeomorphism group; Geodesic distance; Virasoro group

Indexed keywords

EID: 84857458962     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10455-011-9294-9     Document Type: Article

References (12)

1. Arnold V. I.: Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16, 319-361 (1966).
2. Constantin A., Kolev B.: Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78(4), 787-804 (2003).
3. Constantin A., Kappeler T., Kolev B., Topalov P.: On geodesic exponential maps of the Virasoro group. Ann. Global Anal. Geom. 31, 155180 (2007).
4. Fuks, D.: Cohomology of infinite dimensional Lie algebras. Nauka, Moscow (Russian) Fuks D. (1984) Transl. English, Contemporary Soviet Mathematics. Consultants Bureau (Plenum Press), New York.
5. Kriegl A., Michor P. W.: The Convenient Setting for Global Analysis. Surveys and Monographs 53, AMS, Providence 1997 (1984).
6. Michor, P. W.: Some geometric evolution equations arising as Geodesic equations on groups of diffeomorphism, including the Hamiltonian approach. In: Bove, A., Colombini, F., Del Santo, D. (eds.) Phase Space Analysis of Partial Differential Equations. Progress in Non Linear Differential Equations and Their Applications, vol. 69. Birkhäuser, Boston (2006).
7. Michor Peter W., Mumford D.: Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc. (JEMS) 8(2006), 1-48 (2006).
8. Michor P. W., Mumford D.: Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Math. 10, 217-245 (2005).
9. Michor P. W., Ratiu T.: On the geometry of the Virasoro-Bott group. J. Lie Theory 8(2), 293-309 (1998).
10. Misiołek G.: Conjugate points in the Bott-Virasoro group and the KdV equation. Proc. Am. Math. Soc. 125, 935-940 (1997).
11. Ovsienko V. Y., Khesin B. A.: Korteweg-de Vries superequations as an Euler equation. Funct. Anal. Appl. 21, 329-331 (1987).
12. René L.: Schilling: Measures, Integrals and Martingales. Cambridge University Press, New York (2005).